Home field advantage (HFA) is a well-known concept present in most sports, but it contains certain aspects of mystery. While understanding the overall magnitude is trivial with some research, understanding the magnitude of all the contributing factors is not.
The way in which HFA changes over time may give us some clues.
The following is a plot of the average HFA in every football game across the big 5 leagues (England, Spain, Italy, France & Germany) each season since 2014/15.
Thanks to soccerstats.com for data since since 2020 and fbref.com for 2014-2020
Each error bar represents 99% of the possible variance of each season’s HFA. This means there is a 0.5% chance of the ‘real’ value being below the bottom mark of the error bar and a 0.5% chance of being above.
The following details the steps I used to calculate the size of the error bars:
- Consider the standard deviation, s, of home goals and away goals. The poisson distribution is typically used to model football games and assumes the average amount of goals scored is equal to the s of goals scored. I looked at some data and found the s for home goals is actually around ~85% of the mean of home goals and for away goals s is around 95% of the mean of away goals.
- For HFA we want to do home goals – away goals. The standard deviation of a new sample created from the difference of 2 samples is the root of the sum of each standard deviation squared.
- This gives us the standard deviation for HFA for 1 game. For the standard deviation of HFA for n games we divide the standard deviation for 1 game by the square root of n.
- The normal distribution tells us a data point has around a 1% chance of being more than 2.58 standard deviations away from the mean. The size of the upper and lower tail is then 2.58 * our result from 3).
What does this plot tell us?
From 2014/15 to 2018/19 home advantage is buzzing along around the 0.34-0.40 mark. This means if 2 equal teams played each other, the team that had home advantage would win by an average of around 0.34-0.40 goals (the home team would win about 45% of the time with the away team winning only around 30%). Any small variation in these years is explained by natural randomness – each data point would be inside the error bars of the other years.
Halfway through the 2019/20 season, leagues across Europe and the whole world were suspended indefinitely for covid-19. The second half of the 2019/20 and most games during the 2020/21 season were played in front of empty stadiums. VAR was also introduced at the start of the 2019/20 season.
The effect of one or more of these factors is clear in the 2020/21 season because HFA was cut by about 50%. Consider the HFA in 2021 to the HFAs between 2014 and 2019 – it’s clearly statistically significant – in fact the difference has a p value of around 0.000003 (i.e. a very low chance of the drop being explained by randomness).
When fans returned in 2021/22 so did more HFA and in 2022/23 we saw an HFA figure that reached pre covid levels.
This shows some evidence that VAR was not a factor for a reduction in HFA (less opportunity for the referee to be biased to the home team). I say potential because it’s possible the HFA in 2022/23 experienced some positive variance and VAR does have a small part to play in reducing HFA.
The HFA drop when stadiums were empty implies home fans could contribute to the positive effect of HFA by as much as 50%.
2023/24 had an HFA of 0.3 – a little down on the consistent pre-covid numbers but 2024/25 saw a large plummet back down to the same figures as we saw with empty stadiums!
This is very surprising to me as how do we justify it? Total goals per game is not down so HFA is the same fraction of total goals as it always was.
2025/26 is up again so far but the size of the error bar should make it clear that it’s too early to make any conclusions from that.
I plan on adding more leagues to the plot and looking at some more in-depth HFA metrics such as total shots. This will help give further insight and significantly reduce the size of the error bars.
For now, I do suggest analysts or bettors reconsider their figures for HFA if it’s been a year since they did so. The drop in 2024/25 is as statistically significant as the covid induced HFA drop. Are we entering a new era with a fundamentally different home field advantage? Quite possibly!
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Thanks for reading
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